Are you trying to run the game via SDC after it is installed? There should be a start menu shortcut directly to the game you can use if SDC itself doesn't like running under a limited account (if there isn't you can make one--you don't have to use SDC to launch the game in any case).

The game does need an admin account to install and activate, but after that it should be perfectly happy running under a limited account. It won't be able to write the debug.err file, but that won't stop it from running. Everything else it writes is in the user's documents folder.

FYI, SDC is required to download the game, but once you have it installed you can remove SDC if you don't want it around. Major patches will most likey have standalone versions available, though you won't get them as quickly that way as you would using SDC.